UNIVERSITY    OF    CALIFORNIA 

COLLEGE   OF   AGRICULTURE 

AGRICULTURAL    EXPERIMENT   STATION 

BERKELEY,  CALIFORNIA 


Yield,  Stand  and  Volume  Tables  for 
Red  Fir  in  California 


FRANCIS  X.  SCHUMACHER 


BULLETIN  456 

August,  1928 


UNIVERSITY   OF  CALIFORNIA   PRINTING   OFFICE 

BERKELEY,  CALIFORNIA 

1928 


Digitized  by  the  Internet  Archive 

in  2012  with  funding  from 

University  of  California,  Davis  Libraries 


http://www.archive.org/details/yieldstandvolume456schu 


YIELD,  STAND  AND  VOLUME  TABLES  FOR 
RED  FIR  IN  CALIFORNIA 

FRANCIS  X.  SCHUMACHER* 


INTRODUCTION 

Investigations  concerning  the  rate  of  growth  and  yield  of 
California  forests  have,  to  date,  been  confined  essentially  to  the 
species  of  outstanding  commercial  importance.  Although  several 
timber  types  which  are  now  considered  as  of  secondary  value  are 
being  logged  to  a  limited  extent,  demand  for  information  basic  to  the 
management  and  utilization  of  these  is  sure  to  increase  as  logging 
progresses  in  the  more  popular  and  available  types. 

Red  fir  (Abies  magnified),2  including  the  variety  Shasta  fir  (Abies 
magnified  shastensis)  forms  one  of  the  so-called  minor  types.  It 
occurs  at  elevations  of  6000-9000  feet  from  the  Cascade  Mountains  of 
southern  Oregon  southward  along  the  western  slope  of  the  Sierra 
Nevada  Mountains,  and  in  the  Coast  Range  from  Lake  to  Siskiyou 
counties.3  Lying  above  the  main  timber  belt,  it  is  relatively  inacces- 
sible, hence  utilization  has  been  slight,  although  individual  trees  grow 
as  big  and  stands  as  heavy  as  yellow  pine  and  white  fir  on  equivalent 
sites  at  lower  elevations. 

Little  information  is  available  concerning  the  red-fir  type.  In 
California,  it  is  found  mostly  within  the  national  forests,  where, 
according  to  the  estimate  of  the  United  States  Forest  Service,  the 
volume  amounts  to  12,935  million  board  feet4  or  14  per  cent  of  all 
timber  within  the  national  forests  of  the  state. 

The  following  pages  present  the  results  of  a  study  of  the  growth 
of  well-stocked  stands  of  red  fir. 


lAssistant  Professor  of  Forestry. 

2Sudworth,  G.  B.  Check  list  of  the  forest  trees  of  the  United  States.  U.  S. 
Dept.  Agr.  Misc.  Cir.  92:1-295,  1927.  Scientific  names  used  are  taken  from 
this  publication. 

3Red  fir  is  occasionally  confused  with  Douglas  fir  (Pseudotsuga  taxifolia) 
because  the  same  common  name  has  sometimes  been  applied  to  both.  As  Douglas 
fir  occupies  bottomlands  and  slopes  of  low  to  intermediate  elevations,  these 
species  are  never  associated  together.  Botanically  and  commercially  they  are 
very  different  and  should  not  be  confused. 

*Ayres,  R.  W.,  and  W.  Hutchinson.  The  national  forests  of  California. 
U.  S.  Dept.  Agr.  Misc.  Cir.  94:1-34.    1927. 


UNIVERSITY    OF    CALIFORNIA EXPERIMENT    STATION 


GROWTH    OF    RED-FIR    STANDS 

The  growth  of  a  timber  species  is  best  shown  by  tables  which  state 
yields  of  even-aged  stands  over  a  period  of  years  on  lands  of  various 
degrees  of  productivity.  But  density  of  stand — or  approximate 
number  of  trees  to  the  acre  —  as  well  as  age  and  timber-productive 
quality  of  site,  must  greatly  affect  timber  yields.  As  there  is  no 
satisfactory  way  of  expressing  density  in  absolute  terms,  two  types 
of  tables  are  generally  recognized  (1)  empirical  yield  tables  based  on 
density  of  stocking  as  actually  found  over  a  large  area,  and  (2) 
normal  yield  tables  based  on  the  ideal  density  which  produces 
maximum  volume. 

It  is  at  once  evident  that  actual  yields  of  fully-stocked  stands, 
must  be  less  than  the  normal  yields  stated  therefor,  as  the  latter  are 
given  in  gross  values  including  cull  factors,  such  as  decay  in  living 
trees,  unused  stumps  and  tops,  sweep  and  crook  in  logs,  and  breakage 
in  logging.  Only  under  the  best  conditions  of  stand  establishment, 
freedom  from  natural  enemies  and  care,  are  normal  stands  possible 
over  any  considerable  area. 

The  value  of  normal-yield  table  lies  mostly  in  this,  that  they 
furnish  a  basis  for  intelligent  comparison  between  growth  rates  of 
species,  as  comparison  may  be  made  on  equivalent  stocking  as  well 
as  on  age  and  site.  They  also  serve  to  measure  the  degree  of  stocking 
of  any  even-aged  stand  of  the  species  in  question. 


BASIC  DATA 

The  normal-yield  tables  for  red  fir  which  follow  are  based  on 
measurements  of  149  sample  plots  scattered  through  the  geographical 
range  of  the  species. 

Plot  Selection. — Although  little,  if  any,  commercial  logging  has 
been  conducted  in  the  pure  red-fir  type,  many  small,  even-aged 
stands  of  second  growth,  especially  in  the  south-western  part  of 
Plumas  County,  date  from  the  time  of  clearing  or  burning  when 
mining  began  about  75  years  ago.  Older  even-aged  stands  were 
located  through  a  systematic  search  in  the  virgin  timber. 

Within  these  stands,  plots  were  established  so  as  to  enclose  a 
comparatively  complete  crown  canopy  by  excluding  the  larger  open- 
ings which  follow  failure  of  reproduction  or  accident,  and  at  the 
same  time  to  include  within  boundaries  the  area  equivalent  to  that 


BUL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR  5 

which  seemed  to  be  necessary  for  the  growth  of  the  enclosed  timber. 
As  practically  all  plots  were  well  within  large  stands,  this  was  in  the 
main  mechanically  accomplished,  attention  having  been  given  to 
securing  a  clear  sight  from  one  corner  to  the  next  rather  than  to 
balancing  plot  area  with  area  used  by  the  timber.  Rectangular- 
shaped  plots  were  not  sought  though  acute  angles  were,  in  general, 
avoided.  Plots  were  surveyed  with  staff  compass  and  chain. 

Age  Determination. — The  age  of  each  plot  was  determined  by 
counting  the  annual  rings  on  cores  extracted  (with  Swedish  incre- 
ment borers)  from  near  the  base  of  several  trees.  The  number  of 
rings  on  the  core  plus  the  number  of  years  necessary  for  height 
growth  to  reach  the  point  of  boring  (determined  by  an  analysis  of 
height  growth  of  saplings)  was  taken  as  the  age  of  the  tree.  Although 
there  was  seldom  a  difference  of  more  than  two  or  three  years  between 
the  ages  of  the  oldest  and  youngest  tree  examined,  the  age  of  the 
oldest  tree  was  taken  as  the  age  of  the  plot,  as  it  dates  more  nearly 
from  the  time  of  the  removal  of  the  earlier  stand. 

Field  Measurements. — Diameter  breast  high  of  every  tree  was 
measured  with  diameter  tape  and  tallied  by  species  and  crown  class 
(dominant,  codominant,  intermediate,   or  suppressed). 

The  heights  of  fifteen  to  twenty-five  trees  were  measured  with 
the  Forest  Service  hypsometer  and  plotted  over  diameter  on  cross- 
section  paper  in  the  field,  the  number  of  height  measurements 
necessary  being  judged  at  the  time  by  the  range  in  diameters  present 
and  the  dispersion  of  plotted  heights  around  the  free-hand  curve. 

A  short  description  of  physiographic  features  completed  the  field 
work  on  each  plot. 

Office  Computations. — The  computational  work  necessary  for  each 
plot  is  evident  from  following  paragraphs.  The  construction  of  the 
yield  tables  is  after  Bruce,5  while  the  stand  tables  are  based  on 
CharlierV  method  of  calculating  theoretical  frequencies. 

NORMAL    YIELD    TABLES 

Table  1  gives  the  following  data  for  the  entire  stand : 
Site  index:  the   height  that   the   average   dominant   red   fir  will 
attain,  or  has  attained,  at  50  years  of  age.    Height  curves  used  in 
determining  site  index  of  a  plot  are  shown  in  figure  1. 

5Bruce,  D.  A  method  of  preparing  timber-yield  table.  Jour.  Agr.  Research 
32:543-557,  figs.  1-8.    1926. 

«Charlier,  C.  V.  L.  Die  Grundziige  der  mathematischen  Statistik.  pp.  3-125. 
Lutke  und  Wulff,   Hamburg,  1920. 


b  UNIVERSITY    OF    CALIFORNIA EXPERIMENT    STATION 

In  well-established  forestry  practice  it  has  been  found  that  the 
timber-productive  capacity  of  a  forest  area  has  a  closer  relationship 
to  height  of  dominant  stand  for  a  given  age  than  to  any  other  readily 
measurable  factor  of  timber  growth.  In  this  country,  consequently, 
average  height  of  the  dominant  trees  is  now  generally  accepted  as 
the  index  to  site  quality. 

Age :  the  age  of  the  oldest  tree  sampled.  Because  the  establishment 
of  a  new  natural  stand  is  dependent  on  seed  already  on  the  area  when 
the  old  stand  was  removed  by  logging  or  accident — such  as  fire  or 
epidemic  of  insect  or  disease — or  upon  seed  from  neighboring  trees, 
the  new  stand  is  seldom  all  of  one  age. 

Trees  per  acre:  the  number  of  trees  that  have  reached  a  height  of 
at  least  4.5  feet  (breast-height)  above  the  average  ground  level. 

Basal  area  per  acre:  the  sum  of  the  cross-sectional  areas  at  breast 
height  in  square  feet. 

Mean  diameter  breast  high:  the  mean  of  all  tree  diameters  on  an 
average  acre.  It  is  to  be  distinguished  from  average  diameter,  which 
is  understood  to  be  the  diameter  in  inches  of  the  tree  of  average 
basal  area.7 

Height  of  average  tree:  the  height  from  ground  to  tip  of  the  tree 
of  average  basal  area. 

Volume  in  cubic  feet:  the  cubic  volume  of  the  entire  stem  of  all 
trees  from  ground  to  tip  but  without  limbs  or  bark.  The  volume  table 
used  (table  5)  is  given  on  p.  14. 

Average  annual  growth  in  cubic  feet:  the  cubic  volume  of  an  acre 
of  timber  divided  by  the  age.  Maximum  volume  production  is  obtained 
by  allowing  the  stand  to  grow  to  the  age  of  greatest  average  annual 
growth,  which  is  140  to  150  years  in  red  fir. 

Table  2  gives  a  number  of  the  corresponding  values  for  the  trees 
in  the  stand  which  are  8  inches  and  over  in  diameter  breast  high, 
together  with  the  following : 

Volume  in  board  feet:  this  includes  the  board-foot  contents  of  the 
trees  by  the  International  log  rule  of  Vs-inch  kerf  between  a  stump 
height  of  one  foot  and  top  diameter,  inside  bark,  of  5  inches,  scaled 
in  16-foot  logs  with  0.3-foot  trimming  allowance  to  each.  Gross 
volumes  are  presented,  no  account  being  taken  of  cull  factors.  The 
volume  table  used  is  given  on  p.  16. 


?Mean  diameter  is  used  rather  than  average  diameter,  as  the  two  terms  are 
herein  defined,  because  of  association  of  the  former  with  stem  distribution  as 
explained  on  pp.  21  ff. 


BUL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR 


Height  of  average  dominant  in.  feet 
5«f?g>o>oto4s5) 

30000000 


CD  & 

o         o 


3 


I  2 

W  ° 

<x> 

:  >* 

B     OQ. 

a>  0» 

«  o 

g  5' 

Oj  to 

p        fi> 

OQ  P 

«    3  § 


►    \ 

1      \ 

1                     1W 

m^ 

\    \    \   \  ^v 

\       \       \      \       x        *. 

G-VvS 

■      \       l      \      \ 

\       \       \      \ 

TT_Y_\ 

1   \    <_ 

AiX 

vXX 

^            \            \ 

E-M 

G  V- 

ti 

l~WX 

T 

ti  t4 

.  i 

a  tj 

Site  index  in  feet 


UNIVERSITY    OF    CALIFORNIA EXPERIMENT   STATION 


TABLE   1 
Normal  Yield  Table  for  Red  Fir,  Including  All  Trees 


Age 

Height  of 

average 

tree 

Mean 

diameter 

breast  high 

Total 
number 
of  trees 
per  acre 

Total 

basal  area 

per  acre 

Volume 
per  acre 

Average 
annual 
growth 

Years 

Feet 

Inches 

Square  feet 

Cubic  feet 

Cubic  feet 

Site  index  60  feet  at  50  years 


30 

20 

2.5 

1,560 

150 

1,600 

53 

40 

29 

3.7 

1,210 

235 

3,200 

80 

50 

38 

5  3 

957 

295 

5,000 

100 

60 

48 

7.0 

760 

345 

6,950 

116 

70 

59 

9.0 

605 

386 

9.000 

129 

80 

72 

11  2 

478 

420 

11,400 

142 

90 

87 

13.8 

367 

451 

13,850 

154 

100 

103 

16.3 

279 

478 

16,700 

167 

110 

120 

18.8 

214 

502 

20,100 

183 

120 

135 

21  2 

170 

523 

23,900 

199 

130 

148 

23.5 

141 

543 

27,200 

209 

140 

160 

25.5 

119 

559 

30,000 

214 

150 

169 

27.4 

102 

573 

31,900 

213 

160 

177 

29.3 

89 

585 

33,150 

207 

Site  index  50  feet  at  50  years 


30 

17 

2.1 

2,030 

135 

1,250 

42 

40 

24 

3.2 

1,580 

211 

2,600 

65 

50 

32 

4.4 

1,250 

266 

4,050 

81 

60 

40 

5.9 

990 

310 

5,600 

93 

70 

49 

7.6 

790 

347 

7,200 

103 

80 

60 

9.5 

620 

378 

9,050 

113 

90 

72 

11.6 

480 

406 

11,100 

123 

100 

86 

13.7 

362 

431 

13,400 

134 

110 

99 

15.8 

279 

453 

16,100 

146 

120 

112 

17.8 

220 

473 

19,150 

160 

130 

123 

19.8 

181 

490 

21,700 

167 

140 

132 

21.5 

155 

504 

23,950 

171 

150 

140 

23.0 

133 

517 

25,500 

170 

160 

146 

24  3 

116 

528 

26.500 

166 

Site  index  40  feet  at  50  years 


30 

13 

1.7 

3,240 

125 

1,000 

34 

40 

18 

2.5 

2,510 

195 

2,050 

51 

50 

24 

3.6 

1,990 

248 

3,200 

64 

60 

31 

4.7 

1,580 

289 

4,350 

73 

70 

38 

6.1 

1,250 

323 

5,700 

81 

80 

47 

7.7 

990 

352 

7,200 

90 

90 

56 

9.4 

762 

378 

8.800 

98 

100 

67 

11.1 

580 

400 

10,550 

106 

110 

77 

12.8 

442 

422 

12,700 

115 

120 

87 

14  4 

350 

440 

15,100 

126 

130 

96 

16.0 

289 

455 

17,150 

132 

140 

103 

17.4 

246 

469 

18,950 

135 

150 

109 

18  6 

211 

481 

20,100 

134 

160 

114 

19.6 

185 

490 

21,000 

131 

BlJL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR 

TABLE  1 — Continued 


Age 

Height  of 

average 

tree 

Mean 

diameter 

breast  high 

Total 
number 
of  trees 
per  acre 

Total 

basal  area 

per  acre 

Volume 
per  acre 

Average 
annual 
growth 

Years 

Feet 

Inches 

Square  feet 

Cubic  feet 

Cubic  feet 

Site  index  30  feet  at  50  years 


30 

10 

1.3 

5,900 

119 

800 

27 

40 

13 

2.0 

4,560 

185 

1,600 

40 

50 

18 

2.8 

3,600 

234 

2,450 

49 

60 

22 

3.7 

2,860 

274 

3,400 

57 

70 

27 

4.7 

2,290 

306 

4,400 

63 

80 

33 

5.9 

1,810 

334 

5,550 

69 

90 

40 

7.3 

1,400 

358 

6,800 

76 

100 

47 

8.6 

1,050 

379 

8,150 

82 

110 

54 

9.9 

800 

399 

9,800 

89 

120 

61 

11.2 

640 

416 

11,650 

97 

130 

67 

12.4 

525 

432 

13,200 

102 

140 

73 

13.5 

445 

445 

14,550 

104 

150 

77 

14.4 

386 

456 

15,600 

104 

160 

81 

15.2 

337 

465 

16,100 

101 

Site  index  20  feet  at  50  years 


30 

6 

0.9 

10,400 

114 

600 

20 

40 

8 

1.4 

8,150 

178 

1,200 

30 

50 

10 

2.0 

6,400 

225 

1,800 

36 

60 

12 

2.6 

5,100 

262 

2,450 

41 

70 

15 

3.3 

4,050 

294 

3,200 

46 

80 

18 

4.1 

3,220 

320 

4,050 

51 

90 

22 

5.0 

2,490 

345 

4,950 

55 

100 

26 

6.0 

1,880 

366 

5,950 

60 

110 

30 

6.9 

1,430 

385 

7,200 

65 

120 

34 

7.8 

1,130 

400 

8,450 

70 

130 

38 

8.6 

935 

415 

9,650 

74 

140 

41 

9.3 

790 

427 

10,600 

76 

150 

43 

10.0 

690 

438 

11,350 

76 

160 

45 

10.5 

600 

447 

11,800 

74 

Log  run:  the  number  of  logs  to  the  thousand  feet  board  measure 
contained  therein. 


(HECK  OF  BASIC   DATA  AGAINST  YIELD   TABLES 

Table  3  shows  the  check  of  the  values  of  the  149  sample  plots 
against  the  yield  tables  interpolated  to  nearest  year  of  age  and  nearest 
foot  of  site  index. 

That  the  standard  deviation  of  basal  area  is  less  than  that  of  any 
other  variable  is  to  be  expected  as  it  is  the  basis  for  judging  normality 
of  stocking.8   Greater  variation  in  number  of  trees  and  mean  diameter 


s  See  page  18  ff. 


10 


UNIVERSITY    OF    CALIFORNIA EXPERIMENT    STATION 


TABLE   2 
Normal  Yield  Table  for  Red  Fir,  Including  Trees  8  Inches  and  Over 


Age 


Years 


Number 
of  trees 
per  acre 


Volume 
per  acre 


Board  feet 


Average 
annual  growth 


Board  feet 


Logs  per 
M.  B.  M. 


Site  index  60  feet  at  60  years 


30 

16 

800 

27 

30 

40 

87 

6,550 

165 

29 

50 

220 

19,200 

345 

28 

60 

296 

33,700 

545 

25 

70 

328 

50,400 

720 

22 

80 

306 

71,100 

889 

19 

90 

263 

94,300 

1,048 

15 

100 

215 

119,000 

1,199 

11 

110 

176 

145,000 

1,318 

9 

120 

147 

172,000 

1,425 

7 

130 

127 

196,000 

1,508 

6 

140 

111 

216,000 

1,543 

5 

150 

97 

230,000 

1,533 

4 

160 

87 

240,000 

1,500 

4 

Site  index  50  feel  at  50  years 


40 

68 

3,640 

91 

34 

50 

163 

12,000 

240 

33 

60 

287 

23,800 

390 

31 

70 

352 

36,800 

526 

28 

80 

353 

52,000 

650 

24 

90 

313 

70,500 

785 

18 

100 

259 

91,200 

928 

14 

110 

212 

112,500 

1,050 

11 

120 

176 

138,000 

1,145 

9 

130 

152 

156,000 

1,240 

7 

140 

135 

173,000 

1,236 

6 

150 

118 

184,000 

1,227 

5 

160 

106 

191,000 

1,194 

5 

Site  index  Ifi  feet  at  50  years 


40 

25 

1,030 

26 

42 

50 

135 

6,050 

121 

42 

60 

253 

14,400 

240 

41 

70 

388 

25,000 

357 

40 

80 

447 

37,100 

473 

35 

90 

430 

50,200 

588 

26 

100 

368 

65,700 

695 

21 

110 

303 

84,000 

793 

16 

120 

256 

104,500 

871 

13 

130 

226 

122,000 

938 

10 

140 

196 

136,000 

971 

9 

150 

172 

145,000 

967 

8 

160 

154 

151,000 

944 

7 

BUL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR 


11 


TABLE   2— Continued 


Age 


Years 


Number 
of  trees 
per  acre 


Volume 
per  acre 


Board  feet 


Average 
annual  growth 


Board  feet 


Logs  per 
M.  B.  M. 


Site  index  30  feet  at  60  years 


50 

76 

2,100 

42 

53 

60 

211 

6,950 

120 

52 

70 

366 

14,600 

210 

51 

80 

525 

23,600 

295 

49 

90 

588 

33,800 

380 

40 

100 

543 

44,500 

460 

36 

110 

470 

57,700 

538 

26 

120 

410 

72,800 

607 

20 

130 

357 

86,000 

665 

16 

140 

316 

98,600 

705 

14 

150 

282 

108,000 

720 

11 

160 

253 

113,000 

706 

10 

Site  index  20  feet  at  50  years 


60 

77 

1,590 

27 

57 

70 

200 

4,950 

71 

56 

80 

332 

10,300 

129 

53 

90 

487 

17,800 

198 

49 

100 

564 

25,600 

256 

41 

110 

549 

34,600 

315 

32 

120 

520 

44,000 

360 

26 

130 

484 

52,800 

400 

21 

140 

442 

60,400 

430 

17 

150 

409 

67,000 

445 

15 

160 

368 

71,500 

447 

13 

TABLE  3 

Check  Between  Yield  Tables  and  Basic  Data 


All  trees 
per  acre 

Basal 
area 

Mean 
D.  b.  h. 

Volume 

in  cubic 

feet 

Trees 
8  inches 
and  over 

Volume 
in  board 
measure 

+0.74 
33.7 

±1.86 

+0.89 
17.9 

±0.99 

-0  67 
21  5 

±1  14 

+0.53 
20.0 

±1.01 

+0.33 
30.2 

±1.67 

—  1  41 

24.1 

Probable  error  of  yield  table  value — 

±1  34 

*  The  aggregate  difference  is  the  sum  of  plot  values  expressed  as  a  percentage  difference  from  the  sum 
of  corresponding  tabular  values.  

t  Standard  deviation  of  plot  distribution  (<r)=v  _iZ£J  in  which  i=  deviation  of  each  plot  from  its 

N 
tabular  value  to  nearest  year  of  age  and  nearest  foot  of  site  index  in  per  cent,  2  is  the  sum,  and  N  is 
number  of  plots. 

In  a  normal  distribution  about  two-thirds  of  the  number  of  cases  lie  within  plus  and  minus  standard 
deviation  measured  from  the  mean  (in  this  case  tabular)  value. 

X  This  term  is  the  same  as  that  ordinarily  understood  as  probable  error  of  a  mean,  the  mean  here 

being  the  tabular  value  for  age  and  site  index.    It  is  expressed  PE\t=— — 

VN 


12 


UNIVERSITY    OF    CALIFORNIA EXPERIMENT    STATION 


TABLE  4 
Normal  Stand  Table  for  Bed  Fir,  Including  All  Trees 


D.b.  h. 


Age  of  stand  in  years 


40  50 


70 


90  100         110         120        130      140      150 


Number  of  trees  by  diameter  classes 


Site  index  60  feet  at  50  years 


0  0-  2.0' 

252 

122 

67 

37 

22 

12 

7 

4 

3 

2 

1 

1 

2  0-  4.0 

447 

211 

113 

61 

33 

19 

11 

6 

4 

2 

1 

1 

4.0-  6.0 

282 

240 

144 

•   80 

44 

25 

14 

8 

5 

3 

2 

1 

1 

6  0-  8.0 

173 

185 

141 

88 

52 

29 

17 

10 

6 

4 

2 

1 

1 

8.0-10.0 

56 

107 

116 

85 

55 

33 

20 

12 

7 

5 

3 

2 

1 

10.0-12.0 

57 

83 

76 

55 

35 

21 

13 

9 

6 

4 

2 

2 

12.0-14.0 

24 

54 

62 

55 

34 

23 

15 

10 

7 

5 

3 

2 

14  0-16.0 

9 

31 

47 

44 

33 

23 

15 

11 

8 

6 

4 

3 

16.0-20.0 

11 

52 

67 

59 

44 

31 

22 

17 

13 

10 

7 

20  0-24  0 

16 

36 

46 

39 

30 

23 

18 

15 

12 

10 

24.0-28.0 

1 

13 

27 

30 

26 

22 

18 

16 

14 

12 

28  0-32.0 

3 

12 

19 

21 

19 

17 

15 

14 

13 

32.0-36.0 

3 

9 

14 

14 

14 

13 

13 

12 

36.0-40  0 

3 

7 

9 

10 

10 

10 

11 

40  0-44.0 

2 

4 

6 

7 

7 

7 

44.0-48.0 

2 

3 

4 

4 

4 

48  0-52.0 

1 

2 

2 

2 

52.0-56.0 

1 

1 

56  0-60.0 

Total 

1,210 

955 

760 

•605 

479 

367 

280 

214 

170 

141 

119 

102 

89 

Site  index  50  feet  at  50  years 


0.0-  2.0' 

407 

203 

109 

62 

35 

21 

12 

7 

5 

3 

2 

2 

1 

2.0-  4.0 

649 

381 

190 

103 

57 

31 

19 

11 

7 

5 

3 

2 

2 

4  0-  6  0 

328 

329 

243 

132 

74 

42 

24 

15 

9 

6 

4 

3 

2 

6.0-  8.0 

166 

211 

186 

138 

84 

49 

29 

18 

12 

8 

5 

4 

3 

8.0-10  0 

32 

96 

121 

119 

84 

53 

33 

21 

14 

9 

7 

5 

4 

10.0-12.0 

30 

79 

102 

78 

53 

34 

22 

15 

10 

8 

6 

4 

12  0-14.0 

42 

68 

65 

50 

34 

23 

16 

12 

9 

7 

5 

14.0-16  0 

21 

42 

52 

45 

33 

23 

16 

12 

9 

7 

6 

16.0-20  0 

30 

63 

71 

59 

44 

33 

25 

20 

16 

13 

20.0-24.0 

24 

40 

44 

38 

31 

25 

21 

17 

15 

24.0-28.0 

4 

16 

26 

29 

26 

23 

20 

17 

15 

28.0-32.0 

5 

11 

17 

19 

19 

18 

16 

15 

32.0-36  0 

3 

8 

12 

13 

13 

13 

12 

36.0-40  0 

2 

5 

7 

9 

9 

9 

40  0-44.0 

1 

3 

4 

5 

5 

44  0-48.0 

1 

2 

2 

3 

48  0-52.0 

1 

1 

1 

Total 

1,582 

1,250 

991 

796 

620 

476 

361 

278 

221 

181 

155 

132 

115 

BUL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR 


13 


TABLE  4— Continued 


D.  b.  h. 

class 


Age  of  stand  in  years 


40 


90 


100 


110 


120 


130      140      150      160 


Number  of  trees  by  diameter  classes 


Site 

index  Ifi  feel  at  50  years 

0.0-  2.0' 

418 

239 

133 

76 

44 

27 

16 

10 

8 

5 

4 

3 

2  0-  4  0 

766 

434 

229 

128 

71 

41 

25 

17 

12 

8 

6 

5 

4  0-  6  0 

454 

423 

280 

161 

93 

54 

33 

22 

15 

11 

8 

7 

6  0-  8  0 

273 

277 

235 

171 

104 

64 

40 

26 

18 

14 

10 

8 

8.0-10.0 

80 

141 

174 

150 

103 

68 

44 

30 

21 

16 

12 

10 

10.0-12  0 

54 

109 

118 

95 

67 

45 

32 

23 

17 

13 

11 

12  0-14  0 

13 

59 

87 

79 

62 

44 

32 

24 

19 

15 

12 

14  0-16.0 

31 

55 

63 

54 

42 

31 

24 

19 

15 

12 

16.0-20  0 

42 

75 

81 

70 

57 

46 

37 

30 

26 

20  0-24.0 

27 

43 

48 

46 

40 

34 

29 

25 

24.0-28  0 

5 

15 

25 

29 

31 

29 

26 

23 

28  0-32.0 

3 

9 

14 

18 

21 

20 

19 

32.0-36  0 

2 

5 

8 

12 

13 

13 

36.0-40  0 

1 

3 

5 

6 

7 

40.0-14  0 

1 

2 

3 

44.0-48  0 

1 

48  0-52  0 

Total 

1,991 

1,581 

1,250 

988 

759 

579 

443 

352 

291 

248 

209 

185 

Site  index  SO  feet  at  50  years 


0  0-  2.0' 

595 

340 

199 

116 

69 

43 

29 

20 

15 

12 

9 

2.0-  4  0 

1,060 

644 

346 

196 

113 

68 

45 

32 

24 

19 

14 

4.0-  6  0 

667 

597 

423 

248 

147 

90 

59 

42 

30 

24 

19 

6.0-  8  0 

409 

402 

340 

252 

161 

103 

70 

50 

37 

29 

24 

8.0-10.0 

132 

207 

241 

213 

152 

105 

74 

54 

41 

32 

27 

10.0-12.0 

78 

145 

161 

130 

100 

74 

55 

43 

35 

28 

12.0-14.0 

18 

76 

112 

104 

85 

68 

53 

43 

35 

29 

14.0-16  0 

35 

66 

75 

70 

60 

49 

41 

34 

29 

16  0-20.0 

36 

78 

89 

91 

82 

72 

63 

54 

20.0-24.0 

21 

39 

49 

53 

53 

50 

45 

24.0-28.0 

9 

17 

25 

30 

32 

32 

28.0-32.0 

4 

9 

13 

15 

18 

32.0-36.0 

1 

3 

5 

7 

36.0-40  0 

1 

386 

2 

Total 

2,863 

2,286 

1,805 

1,400 

1,050 

801 

640 

525 

445 

337 

Site  index  20  feet  at  50  years 


0.0-  2  0' 

1,020 

584 

336 

202 

129 

86 

62 

47 

37 

30 

2.0-  4  0 

1,670 

1,100 

627 

350 

219 

142 

100 

75 

58 

47 

4.0-  6.0 

862 

795 

662 

431 

275 

180 

131 

98 

76 

62 

6  0-  8.0 

407 

487 

448 

356 

267 

203 

144 

110 

87 

71 

8.0-10  0 

102 

208 

249 

255 

218 

169 

136 

109 

89 

74 

10.0-12.0 

42 

115 

157 

153 

135 

116 

99 

86 

73 

12.0-14.0 

40 

86 

99 

100 

93 

82 

74 

64 

14.0-16.0 

10 

43 

57 

64 

67 

65 

61 

55 

16.0-20.0 

14 

52 

69 

75 

79 

76 

20.0-24  0 

17 

27 

35 

37 

24.0-28.0 

4 

8 

11 

28.0-32.0 

1 

Total 

4,061 

3,216 

2,487 

1,880 

1,431 

1,131 

935 

791 

690 

601 

14 


UNIVERSITY    OF    CALIFORNIA EXPERIMENT    STATION 


3 


CO    O    »    Ifl    W    N  OO    Tt<  O     OS    W5    "5  CM    OiN    N    CO    O  CO  CM    <M  CO  CO     CM 

«    «     M     N    «    MM    «N     "H     —■    — l  —I     i-l 


NMO  O  lONOlO'OlOOm  oooo 
N  .-I  lO  OS  MNNNNNCOOO  -*<  O  S  CO 
CM  CO  CO    CO    ■*  *  «S  K5  tD  ID  N  N    00  OS  OS  O 


o  co  oo  «5  loifltoioomio")  o 


•«»<   Nno 


O 

cc 
«o 

ia 

o 

iO 
to 

to 

OO 

CO  O 
c©  N 

O  "5 

N  CO 

■Offl 

HMD 
bJ  CO 

n  oo 

ooo 
nn 

© 

«* 

OS 

N 

CO 

CO  OS  ■»*< 

■*  CD  OS 

co-<*<  oo 

CO  "ON 

-H  O  CM 

CM  Tfl  CO 

ON* 
pH  CM  "^ 

O 

oo-«*<o 

CS-ICO 

ooo 
omoo 

CM  CM  CM 

rt  00  CO 
OCNO 
CM  CM  CM 

CO  00  CO 
00  O  CO 
-H  CM  CM 

o 

CO 

IC 

oo 

CM 

o 

CO 
CM 

co 
co 

CM 
OS 

o 

CM 

iflOiOXSWiOOiO 
t*HOO-HU002COOOCM 
COCO^^^fOlOCO 

N00OOU5OOO 

rt>tc«NlOOiMN 
COCOCO-^^T^lOlO 

O 
N. 

cc 

o 
o> 
t~ 

•o 

o 
N 

CO 

o 
to 

CO 

oa 

o 
oo 

OONOliHlOMOO 
OO-H^OOi-lTtlOOCM 
CM  CO  CO  CO  ■*■«*<■«#  »C 

oo 

CM  oo 

\ti  "0 

coo 

CO  CM 

"5  "5 
CO  N 

ICO 

N  •* 

»0  CO 

locoo 

CO  00-* 

00  N  N 

■<*<  CO  oo 

OOCOOOOOOOCM 
lO00»HTtlt-~O5COCO 
(N  IN  M  CO  CO  CO  ^  t 

n  co 

cs    CO 

ncm 

CM  CO 

CO 

co 

CO 

H-<*l00"0lONlO-*f< 

COlONO'^'fiOO'- 1 
CMcMCMCOCOCOCO-^ 

iQ-OO 
c5  OS  »C 
N-  OO  00  OS 


r^^co-H 

CONN00 


OkOOiO 
COCO  t- 


OOCOU) 
I  COO 


iOO"OlO 

osco  coo 

■**  "0  »C  CO 


CO    CD    MO    CO 


O  "5    O  O    O    m    "O 

co  Ice  i_ 
n|oo  o  -h 


oo    n    OO  CM    00    "i    CO  lO    NkO    lOliO    lO  o  o 

■^    t>-    O  ■"*    N    l-i    iflO)    COOO    colco    ■>*<  CO  OS 
-1    i-H    CM  CM    CM    CO    COCO    ■«*<  ■"*    uolco    N  00  OS 


o  t-  >o   cm 

CO  •>*  CO    oo 


INCONWON* 


l-«J<  coo 
JNO-c* 


00  CO  COO 
00  -*  ^IN 
CO  -^  ^  ^ 


i-l  t-l  CM  CM  CM  CM  CM  CO    CO  CO  CO  « 


NCO    N    O    Ml 


CO  UO    CO  O    ■*    O 


Ifl    N    CO    OO    ■*! 


"0    O  O  O    o 


-<*l  >o 

C--  r4    ifj    Tti    ■*  -«*i  lO    N«N  U0  O  "5  t-h  N  "0  "*  CM  >-H  OOJiO 

CO-*     •«*<    «5     *M»    »ON  CO  10CD  OO  OS  iH  CO  »«  N  OS  rH  CO  "0 

«— ih  »— I  »— I  t— li— 1»— IcMCMcMCM  CMCOCOCO 


O    O     >0     O    "5     O    O 


-H     CM     CO     Hi 


-H     CO     N 


OO    CO  O    OS  00    H 
N    OS  -H     CM  •**<     N 


CM     CO    >0     O  < 


00    CO  OS     ifi  CO    CM 
CO    00  OS     »-l  CO    »C 


N    OS 


oo 

00 

~t< 
-* 

CO 

CM    CO 
OO    0O 

a 
a 

lO  o 

La 

~- 

<M 

CO 

oo 

O) 

o 

CO    •»* 

N     OS 
CM    O 

>o 

N  00 

r' 

CO 

N 

4j 

CM 

lo 

"0  oo 
O-H 

>o 

CO 

""* 

*■■ 

CI 

CO    •«*< 

Lq 

CON 

oc 

CM 

CO 

CM 

o 

a 

o 

oo  |>o 
co  Ico 

OJ 

00 

C3> 

^ 

^ 

CJ 

CM  IcO 

41 

■«*< 

-*<OS 
CM  •** 

o 

I- 

s 

O    CO 

-!• 

CM    CM 

t-«o 

-H  CO 

>o 

00 
OO 

N 

CO 

CM  CO    ■<*<    lO    CO    N    00 


OH    NM    *    lO    (ON    OOO    O 


s« 


BUL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR  15 

is  the  outcome  of  variation  in  the  time  between  full  stocking  of  the 
sample  plots  and  measurement.  A  stand  that  has  been  fully  stocked 
over  a  period  of  several  decades  distributes  its  growth  over  many 
trees  with  a  consequent  dropping  off  in  diameter  growth  of  the 
average;  whereas  a  stand  of  fewer  trees  that  has  but  recently  closed 
its  crown  canopy  has  also  but  recently  approximated  full  stocking 
by  basal  area,  and  its  growth  is  distributed  over  fewer  trees  to  the 
greater  advantage  of  each.  It  follows  that  a  stand  fully  stocked  by 
basal  area  may  be  made  up  of  many  slender  trees  or  comparatively 
few  stout  ones,  hence  the  greater  variation  in  number  of  trees  and 
mean  diameter. 

STAND  TABLES  FOR  RED  FIR 

Although  yield  tables  are  basic  to  the  solution  of  many  forest 
management  problems  in  a  given  timber  type  in  that  they  express 
either  total  or  average  values  attainable  in  properly  established  and 
protected  stands,  they  are  not  complete  without  stand  tables,  which 
state  the  number  of  trees  to  be  expected  within  each  diameter  class,  as 
problems  of  valuation  and  utilization  require  knowledge  of  such  stem 
distribution. 

Stand  tables  for  red  fir  are  given  in  table  49. 


VOLUME  TABLES    FOR    RED    FIR 

Preliminary  to  the  study  of  yields  in  cubic  and  board  feet,  volume 
tables  in  these  units  were  prepared.  The  basic  tree  data  of  the  tables 
presented  are  from  measurements  taken  by  the  Division  of  Forestry 
in  Plumas  and  Sierra  counties  from  several  previously  measured, 
even-aged  sample  plots.  The  ages  of  the  trees  measured  were  from 
30  to  110  years  on  the  stump. 

Table  5  is  the  volume  table  in  cubic  feet,  and  states  the  entire 
volume  of  the  stem,  including  stump  and  top,  but  without  bark.  It 
was  prepared  by  the  form-factor  method. 

Table  6  is  the  volume  table  in  board  measure.  It  includes  the 
board-foot  contents  of  the  trees  between  a  one-foot  stump  and  top 
diameter  inside  bark  of  five  inches.  It  was  prepared  from  an  analysis 
of  the  board-foot — cubic-foot  ratio  of  the  trees. 


9The  analysis  of  stem  distribution  and  construction  of  stand  tables  is  explained 
in  pp.  21  ff. 


16 


UNIVERSITY    OF    CALIFORNIA EXPERIMENT    STATION 


ffl.8 
S 


NiooofainoiMN  Hinon 


CM  CM    CM    MCOW*' 


i  1*1  m  m  (o<otot^ 


ooo  o  oooooooo  oooo 

1*1  OS  if    O  OKDOO-HCCr-rtOO  lOONi1 

Oi  >— I  if    t^-  0>  N  1(5  05  N  «5  05  (N  COO^OO 

t-h  CM  CM*   CM  C<ToOCOC«3  -^"if "*«0  lOlOO* 


ooo  ooo  o  oooooooo  oooo 

C&0000    OOOO    O    i«  CM  O  O  O  CM  •*  03    CO  o  CO  lO 
HMU5    t>- O  CM    >C    NOCOIOOIINIOX    N!D»CC 


•  O  CO  CO  Ol  (M  1(5 
,_(    _i,h,_!    rtiMN    CM    CM  cO~CO  CO~CO  if -<f  "<*    »«  "3  "5  CD 


O    O  O  «5 

rt    NMO> 
»0    "5  CO  CO 


OOOOO 


O    OOO    OOO    O    OO    _ 

"      g  32  S  »"  Q  9°  ??  ¥5 


OS    OM*    COC 


CM    K5NOCN10  00. 


I  CM    CM    CM  CM  CO  COCO  < 


OOO    OOO    O 

to  cm  oo  m  ->f  co  co 

OS  t-c  CM    "*  CO00    O 


OOOOOOOO  OOOO 
KJOOOUS'HOO^CO  CM  O  CM  »« 
CM  if  t--  OS  CM  ■**!  t~  O    CO  CO  OS  CM 


OCDO    O    OOO    OOO 
i-H  co  CM    1*1 
lO  lO  CO    t~- 


CM  CM  CM  CM  CO  CO  CO  if    i*<  if  ' 


O  ooo< 

CO    CO  if  lO  <_    . 

00    O  O  ■*  N  CR  >H  *  CO    05CM- 


-1    (M  (M  CM  CM  CM  CO  CO  CO    CO- 


i-lHrtNN    <M 


CO   i*l   oot^uo   t--   mioo 

CO    O    *»■*    1*1    UJNO 
CO    ■*    if  if  lO    CO    t-ooo 


co  o  oooo  o  >omo 
*-h  ic  cecot-  co  ioiot> 
CO    CO    «■*•*    lO    cot^oo 


ooo  o  oooooooo  oooo 
->f  oo  co   o>   conOHHHNcc   iocbcoks 

'HCNi*    lO    t^  CT2  hH  CO  >Cl  t-  CT>  «H    CO  "O  00  O 


I  CM  CM  CM  CM  CM  CO    CO  CO  < 


lOOO    o    OOOOOOOO    oooo 
00  i-l  1*1    r-    NcO-HOOiOMOlh-    lO  CO  CO 
OS  i-c  CM    CO    lO  CO  00  OS  .— I  CO  if  CO    00  O  CM 


I  CM  CM    CM  CO  CO  CO 


rtiO  ^h    O 


l  O  ^    CM    1*1  ! 


OOOOOOOO 


OOO 

_     CO  -H        - 

ncON    00  050    *H    NCO^CONOOOrt    CO  1*1  CO  t^ 


IHU5O0NN 

I  CM  CM    CM  CM  CM  CM 


mom  >omo  m  oooooooo  ooo< 

CM  Oi  CO    MHO    OO    00  00N00  0)05ON    CO  *0  CT>  < 
■**U)    CO  t^  0O    00    OlOHMM^CON    OOOlOl 


f^  Oi  «— I  CO  OO  CO  < 


I  CO  if  1*1  iC  CO  CO 


•  00  OS  O  O  —l  CM  CO 


!»■*  «)  CO  N 


OVO  CM  1*1  CO  C 


O  CM  1*1  CO 


l  CM  CM  CM  CM  CM  CO  CO  CO  CO  CO 


§9 


ifcOOOOCM    TftOoOO 

1*1  if  if  io  io  ifliomco 


BUL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR 


17 


Table  7  shows  the  check  of  the  basic  tree  data  with  the  volume 
tables. 

TABLE  7 
Check  Between  Volume  Tables  and  Basic  Data 


Cubic  foot 
volume  table 

Board  foot 
volume  table 

+0.17 

8.9 

±0.35 

-  0.43 

16.2 

Probable  error  of  volume  table  value — 

±  0.69 

APPENDIX 


BASIC    DATA 


The  sample  plots  on  which  the  yield  and  stand  tables  are  based 
were  measured  by  the  Division  of  Forestry  in  1926.  Out  of  156  plots 
originally  measured,  7  were  discarded  for  reasons  to  be  discussed 
later.  The  149  actually  used  are  from  the  watersheds  listed  in  table  8. 


TABLE  8 
Distribution  op  Plots  by  Principal  Watersheds 


Watershed 

Number 
of  plots 

2 

Upper  Sacramento  River 

Battle  Creek..  .. 

20 
1 

51 

31 

9 

6 

1 

1 

Upper  San  Joaquin  River 

27 

Total 

149 

The  composition  of  the  plots  by  basal  areas  of  the  various  species 
included  is  shown  in  table  9. 


18 


UNIVERSITY    OF    CALIFORNIA EXPERIMENT   STATION 


TABLE  9 
Composition  by  Basal  Area  of  the  Plots  Used 


Species 

Basal  area 

in  percentage 

of  total 

Red  fir 

97.41 

White  fir 

2.24 

0.23 

0.08 

0.03 

Incense  cedar  and  sugar  pine... 

0  01 

Total 

100.00 

The  distribution  of  the  plots  by  site  and  age  classes  is  given  in 
table  10. 

TABLE  10 

Distribution  of  Plots  by  Site  and  Age  Classes 


Site  index- 

-height  in  feet  of  the  average  dominant  tree  at  50  years 

16-25 

26-35 

36-45 

46-55 

56-65 

Total 

26-  35 

1 
1 
4 
5 
2 
7 
3 
6 
4 

2 

I 

4 

36-  45 

2 

46-  55 

11 

7 

5 

56-  65             

4 
1 
5 
6 
5 
2 

20 

66-  75 

1 

3 

14 

76-  85               

12 

86-  95 

3 

3 

10 
2 
6 
6 
5 
9 
2 
3 

3 

18 

96-105                  

23 

106-115               

8 

116-125               

6 

126-135 

3 

1 
2 

10 

136-145 

7 

146-155 

i 

1 

11 

156  165 

3 

166-175    

2 

1 

6 

Total 

5 

25 

39 

67 

13 

149 

REJECTION    OF    ABNORMAL    PLOTS 

The  analysis  of  the  data  for  abnormalities  was  based  on  (1)  basal 
area  to  the  acre,  (2)  number  of  trees  to  the  acre,  and  (3)  mean 
diameter  breast  high. 

Basal  Area.— Preliminary  curves  of  basal  area  over  age  were  fitted 
to  the  data  of  the  original  156  plots  and  the  percentage  deviation 
of  each  plot  from  the  curves,  interpolated  to  nearest  year  of  age  and 
nearest  foot  of  site  index,  arranged  as  in  table  11. 


BUL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR 


19 


TABLE  11 

Deviation  of  Actual  Basal  Area  of  Plots  From  Theoretical  Basal  Area  of 

Preliminary  Curves  Taken  to  Nearest  Foot  of  Site 

Index  and  Nearest  Year  of  Age 


Percentage 
deviation 

Number 
of  plots 

-35  to  -44 

2 

-25  to  -34 

11 

-15  to -24 

26 

-  5  to -14 

40 

5  to  -  4 

26 

6  to      15 

23 

16  to     25 

15 

26  to     35 

7 

36  to     45 

6 

Total 

156 

The  standard  deviation  of  distribution  is  18.2  per  cent.  Four 
plots  which  exceeded  two  standard  deviations  (36.4  per  cent)  from 
the  mean  for  age  and  site  index  were  scrutinized  in  order  to  discover, 
if  possible,  a  reason  for  their  high  deviation.  One  boundary  of  two 
of  them  was  partly  in  the  open,  and  because  of  the  possibility  that 
this  boundary  of  each  was  drawn  in  too  close  to  the  timber,  giving 
exaggerated  figures  on  the  area  basis,  these  two  were  discarded. 

Number  of  Trees. — Percentage  deviations  in  number  of  trees  of 
the  remaining  154  plots  from  the  curved  number  of  trees  for  age  and 
site  index  were  next  computed  and  are  shown  in  table  12. 


TABLE  12 

Deviation  of  Actual  Number  of  Trees  on  Plots  From  Theoretical  Number 

of  Trees  of  Preliminary  Curves  Taken  to  Nearest  Year  of 

Age  and  Nearest  Foot  of  Site  Index 


Percentage 
deviation 

Number 
of  plots 

-46  to  - 

-65 

13 

-26  to  - 

-45 

28 

-  6  to  - 

-25 

32 

14to- 

-  5 

29 

15  to 

34 

23 

35  to 

54 

13 

55  to 

74 

7 

75  to 

94 

4 

95  to 

114 

3 

115  to 

134 

1 

135  to 

154 

1 

Total. 

154 

20  UNIVERSITY    OF    CALIFORNIA EXPERIMENT    STATION 

The  standard  deviation  of  distribution  is  40.0  per  cent,  and  the 
deviation  of  seven  plots  exceeded  twice  the  standard  deviation.  On 
examination  of  these  it  was  found  that  five  contained  a  high  per- 
centage of  trees  in  the  low-diameter  classes,  indicating  a  possibility 
of  the  presence  of  two  age  classes.  These  five  plots  were  accordingly 
discarded. 

Since  no  abnormal  plots  were  discovered  in  the  analysis  of  devia- 
tions of  mean  diameter  breast  high,  the  remaining  149  plots  were 
used  in  the  construction  of  the  yield  and  stand  tables. 

THE    EFFECT    OF    PLOT    AREA 

At  the  time  each  plot  was  located,  effort  was  made  to  enclose,  as 
nearly  as  could  be  judged,  the  equivalent  of  the  area  occupied  by 
the  growing  timber  within  plot  boundaries.  The  personal  factor  may 
have  played  a  small  part  in  the  location  of  boundaries  with  respect 
to  boundary  trees,  but  where  practically  all  plots  were  well  within 
larger  stands,  as  is  the  case  with  the  red-fir  plots,  the  resulting  error 
is  probably  negligible.  Table  13  shows  the  distribution  of  plots  by 
area  classes. 

TABLE  13 
Distribution  of  Plots  by  Area  Classes 


Area  in  acres 

Number 
of  plots 

Less  than  0.100  acre 

25 

0.100-0.199 

53 

0.200-0.299 

41 

0.300-0.399 

24 

0.400-0.499 

8 

0.500-0.599 

1 

0  600-0.699 

3 

0.700-0.799 

1 

Total 

149 

Average  acrea  in  acres 

0.222 

The  correlation  coefficient  (r)  between  plot  area  and  plot  basal 
area  as  a  per  cent  deviation  of  yield  table  basal  area  for  age  and  site 
was  found  to  be 

r  =  —  0.22  ±0.053 

indicating  that  with  increase  of  plot  area  there  is  a  tendency  toward 
decrease  in  basal  area  to  the  acre,  the  59  plots  having  an  area  greater 
than  0.25  acre,  average  3  per  cent  less  basal  area  to  the  acre  than 
the  yield-table  figures.    The  reason  for  the   correlation,   though  of 


BUL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR  21 

little  significance  in  this  case,  is  important  in  sample-plot  work. 
Should  all  plots  have  been  of  the  same  size?  It  is  not  probable  that 
the  boundaries  of  small  plots  were  drawn  in  too  close  to  the  trees, 
because  special  care,  combined  with  previous  experience  in  work  of 
this  nature,  was  taken  with  them.  Suitability  of  plots  as  samples  was 
judged  by  number  of  trees  thereon,  after  the  stand  was  deemed  of 
about  normal  stocking  and  found  to  be  even-aged,  and  not  by  area. 
It  was  assumed  that  100  to  200  trees  would  be  representative  of 
diameter  distribution  for  site,  age,  and  density,  and  the  enclosing  of 
about  these  numbers  was  sought  regardless  of  size  of  timber;  hence 
plots  small  in  area  are,  as  a  rule,  samples  of  small  timber.  Where 
rather  abrupt  changes  in  density  occurred  in  such  stands  the  policy 
of  locating  two  or  more  plots  therein,  each  consistent  in  its  own 
density,  was  adopted.  Thus  average  density  of  small  plots — hence 
plots  of  small  timber — is  made  up  of  a  wide  range  in  the  density  of 
individual  plots. 

In  large  timber,  small  plots  are  scarcely  acceptable,  for,  on  account 
of  the  size  of  individual  trees  and  distance  between  them,  there  is  less 
assurance  that  plot  area  is  equivalent  to  the  area  occupied  by  the 
enclosed  timber.  As  plots  are  enlarged,  however,  especially  when 
boundaries  are  entirely  within  the  stand,  their  areas  approach  true 
stand  area  more  certainly. 

An  ocular  estimate  was  made  in  the  field  of  the  stocking  of  each 
plot  by  basal  area  and  this  was  later  compared  with  actual  stocking. 
The  correlation  coefficient  between  estimated  and  actual  stocking  is 

r  =  0.68  ±  0.038 

which  is  satisfactory,  since  the  basis  of  ocular  comparison  (100  per 
cent  stocking)  had  not  yet  been  worked  out.  The  correlation  shows 
that  dense  plots  were  usually  known  to  be  dense  at  the  time  of  meas- 
urement and  yet  were  considered,  in  the  field,  acceptable  as  basic 
data  for  the  yield  study.  Furthermore  most  of  the  denser  plots  were 
considered  among  the  surest  measured,  in  that  boundaries  might 
have  been  changed  at  will  without  affecting  the  average  spacing  of 
the  enclosed  timber. 


CONSTRUCTION   OF   THE   STAND   TABLES 

If  the  distribution  of  number  of  trees  by  diameter  classes  follows 
the  normal  curve  of  error,  the  construction  of  stand  tables  becomes 
relatively  simple,  as  it  is  based  on  but  two  constants,  (1)  mean 
diameter,   and    (2)    standard   deviation   of   distribution.    If,   on  the 


22  UNIVERSITY    OF    CALIFORNIA EXPERIMENT    STATION 

other  hand,  frequency  distribution  is  not  normal,  the  computation 
of  at  least  two  other  constants  becomes  necessary,  namely  (3)  a 
measure  of  skewness  or  the  departure  from  symmetry  of  distribution, 
and  (4)  a  measure  of  kurtosis  or  excess,  that  is,  the  form  of  the 
frequency  curve  in  the  general  region  about  its  central  tendencies, 
which  may  be  pointed  or  flat-topped,  rather  than  normal. 

It  is  obvious  that  the  numerical  values  of  these  constants  must 
progress  smoothly  with  increase  of  age  for  a  given  site  index,  and 
with  site  index  for  a  given  age.  At  once  the  question  comes  up  as  to 
whether  the  last  three  constants  of  distribution  may  not  show  as  high 
correlation  with  the  first,  the  mean  diameter,  as  with  age  and  site, 
since  these  variables,  in  stands  of  normal  density,  may  be  considered 
as  causal  factors  of  mean  diameter  itself.  If  that  is  true  the  compu- 
tational work  may  be  considerably  lessened,  as  fewer  curves  would 
be  required. 

The  constants  may  be  considered  separately: 

Mean  Diameter. — This  must  necessarily  be  correlated  with  age 
and  site  as  given  in  table  1. 

Standard  Deviation. — Standard  deviation  of  stem  distribution 
was  correlated  (1)  with  age  and  site,  and  (2)  with  mean  diameter. 
Percentage  deviation  of  the  standard  deviation  of  each  plot  from  the 
two  curved  standard  deviations  was  next  computed  and  analysed 
with  the  following  results: 

( 1 )  Standard  deviation  of  plot  standard  deviations,  measured  from 
the  curves  of  standard  deviation  for  age  and  site  index=20.9  per  cent. 

(2)  Standard  deviation  of  plot  standard  deviations,  measured 
from  the  curve  of  standard  deviation  for  mean  diameter  =  21.1 
per  cent. 

It  becomes  apparent  that  the  correlation  of  dispersion  with  mean 
diameter  is  as  high  as  it  is  with  age  and  site. 

Skewness. — In  the  trial  correlation  of  skewness  with  age  and  site 

as  against  mean  diameter,  skewness  of  each  plot  was  computed  by 

the  formula. 

3(M-Md) 

skewness  =  — 

a 

in  which  M  is  mean  diameter,  Md  is  median  diameter  and  o-  is 
standard  deviation.  This  formula  combines  sufficient  accuracy  with 
ease  of  calculation,  and  as  the  calculated  quantity  is  in  terms  of 
standard  deviation,  skewness  of  large  timber  is  comparable  with  that 
of  small.  Correlated  with  (1)  age  and  site,  and  (2)  mean  diameter, 
following  is  the  comparison: 


BUL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR  23 

(1)  Standard  deviation  of  skewness  of  the  stem  distribution  of 
each  plot  measured  from  the  curve  of  skewness  for  age  and  site 
=  0.446. 

(2)  Standard  deviation  of  skewness  measured  from  the  curve  of 
skewness  for  mean  diameter  —  0.398. 

In  this  case  there  is  apparently  closer  relationship  between  skew- 
ness and  mean  diameter  than  there  is  between  skewness  and  the 
age-site  variables. 

Kurtosis. — Since  kurtosis  or  excess  of  each  plot  is  based  on 
moments  higher  than  that  from  which  standard  deviation  is  derived 
with  consequent  greater  probable  error  of  its  calculated  value,  no 
trial  measure  of  kurtosis  was  correlated  with  site  and  age,  as  against 
mean  diameter. 

Stand  Tables  Based  on  Mean  Diameter. — As  the  correlation  of 
standard  deviation  is  as  high  with  mean  diameter  as  with  age  and 
site,  distribution  of  stems  may  be  considered  as  independent  of  the 
latter  variables,  except  in  so  far  as  age  and  site  are  causal  factors  of 
mean  diameter.  Given  two  stands,  then,  of  common  mean  diameter, 
one  of  good  site  quality  but  young,  the  other  of  poor  site  quality  and 
perhaps  60  years  older,  the  form  of  their  stem  distribution  curves 
should  be  identical. 

The  plots  were  therefore  sorted  into  2-inch  mean-diameter  classes. 
But  in  order  to  prevent  greater  than  actual  range  in  diameters  on 
account  of  such  rather  broad  grouping,  frequency  by  diameter  class 
of  each  plot  was  taken,  not  by  frequency  in  each  one-inch  diameter 
class,  but  by  frequency,  in  percentage  of  total,  in  each  unit  of  one- 
half  standard  deviation  measured  from  mean  diameter.  This  was 
easily  accomplished  by  constructing  a  cumulative  frequency  curve 
for  each  plot  and  marking  it  at  the  upper  limit  of  each  one-half 
standard-deviation  unit  (fig.  2).  By  subtraction  between  upper 
limits  of  adjacent  units,  cumulative  frequency  was  broken  down  into 
ordinary  frequency. 

After  trial  by  Pearson's10  and  Charlier's11  methods  of  fitting 
frequency  curves  to  distributions,  the  "Type  A"  of  the  latter  was 
adopted  because  less  volume  and  exactness  of  computational  work  is 
involved.  With  Pearson's  "Type  I"  system  into  which  all  the  dis- 
tributions fall,  the  interdependence  of  half  a  dozen  constants  calls 
for  the  use  of  calculating  machines  for  computations  to  several 
decimals — a  volume  of  work  not  warranted  by  the  accuracy  needed. 


loElclerton,    W.    P.     Frequency   curves   and    correlation,     pp.    1-167.    Layton, 
London.    1906. 

nCharlier,  C.  V.  L.    Die  Grundziige  der  raathematischen  Statistik.    pp.  3-125. 
Lutke  und  Wulff,  Hamburg.    1920. 


24 


UNIVERSITY    OF    CALIFORNIA EXPERIMENT   STATION 


Charlier's  "Type  A"  frequency  fits  distributions  which  are 
unimodal  and  not  extremely  asymetrical.12  The  following  constants, 
with  mean  diameter,  are  required: 


100 


90 

t 

1.70 


x60 

t 

C 
ft) 

£  40 
■??  jo 


|  20 
«    .0 


Site  index  45ft. 
Age             ^oyrs 

Mear\d.b.h5".9*m- 
= Upper  limit  of 
each  ^standard 
deviation  class 
Interval. 

Ur         6        6        10       ia        14-        16        Id 
Diameter  breast  high  in  inches 


20     2.2 


Fig.  2. — Graph  of  cumulative  frequency  of  number  of  trees  of  a  sample  plot, 
showing  a  step  in  the  conversion  of  frequency  by  diameter  class  in  inches  to 
frequency  in  units  of  one-half  the  standard  deviation. 

12  Charlier's  "Type  A"  frequency  curve  has  the  form 

N   \  ] 

F(x)=—  U0(z)+/Wz)-f/M>4(z) 
a    I  > 

in  which 

F(x)  =  frequency  of  x  (in  this  case  frequency  per  unit  of  one-half  standard 

deviation  measured  from  mean  diameter). 
N       =  total  frequency. 
a        =  standard  deviation. 

1      -x2 


*,(*)  =V^e-T 


>*(x) 


d3<f>o 
:  dx* 
.rfVo 

dxi 


These  are  tabulated  for  unit  frequency  with  x  in  terms 
of  standard  deviation  in  Charlier,  loc.  cit.  pp.  123-125. 


Coefficient  of  asymetry,  /33=  —  -x\  ( 


6trJ 


Coefficient  of  excess,  /34 


_  1  (v,    , 

_2lV74     ' 


)    (F4- 


the    3rd    moment    measured   from 
mean). 


the 


the  4th  moment  measured  from  the 
mean). 


BUL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR 


25 


(1)   Standard  deviation  (fig.  3).    The  plotted  points  are  weighted 
means  of  individual  plot  values  with  standard  deviation  in  inches. 


A  9 


ce 


•  ~  7 


i 
9 

\ 

I 

/>a 

II 
/ 

^ 

5^ 

^  1 

-°5 

\ 

\ 

> 

/      . 
1/ 

\ 

I 

10 

1 s 

i/ 

13 

// 

/* 

1U& 

'As 

I9> 

l5<^ 

7 

I 

0 
0         Z         4  6         ©  »o        12        14        16         18        20       22       24       26       26      30      32 

Mear\  diameter  breast  high  in  inches 
Fig.  3. — "Relation  between  standard  deviation  and  mean  diameter  of  stand. 

(2)  Coefficient  of  asymetry  (/33)  (fig.  4).  These  were  computed 
after  plots  were  grouped  by  2-inch  mean-diameter  classes  and  fre- 
quencies in  units  of  one-half  standard  deviation. 


IS         14         16         16         20       22        ZU-       26        26       30       32 

Mean  diameter  breast  high  m  inches 
Fig.  4. — Relation  between  coefficient  of  asymmetry  and  mean  diameter  of  stand. 


26 


UNIVERSITY    OF    CALIFORNIA EXPERIMENT   STATION 


(3)   Coefficient  of  excess  (/?4)   (fig.  5).    These  were  also  computed 
after  the  latter  grouping. 


02 


^     02 


N, 

19 

/V 

15 

<\ 

V 

15 

)^Co 

{/ 

\ 

a*\ 

15 

<^ 

•v      IO 

"■2 

10 

5^ 

"H 

2 

"^P- 

5 

U  6  &  10         12         14         16         18        20        22 

Mear\  diameter    breast   K\gk  irv  inckes 


24       26       28       30       32 


Fig.  5. — delation  between  coefficient  of  excess  and  mean  diameter  of  stand. 

From  the  calculated  frequencies  for  each  2-inch  mean  diameter 
the  values  of  table  4  were  calculated  by  transcribing  percentage 
frequencies  to  number  of  trees  according  to  the  mean  diameter  and 
total  number  of  trees  for  a  site-age  class  as  given  in  table  1. 


RELATIONSHIPS   WITHIN    THE   STAND 

If  it  is  possible  to  express  the  stocking  of  an  even-aged  stand  in 
terms  of  probable  maximum  stocking  for  site  and  age  of  the  species 
in  question,  a  quantitative  measure  of  the  mean  stocking  of  the  basic 
plots  used  in  the  construction  of  the  yield  tables  of  the  species  is  the 
first  requirement.  Now  it  is  evident  that  stocking  by  basal  area  or 
volume  depends  not  only  upon  number  of  trees  to  the  acre  for  age 
and  site  but  upon  average  size  of  the  trees  as  well.  But  since  average 
size  of  tree  can  be  controlled  only  indirectly  by  limiting  the  number 
of  trees  to  the  acre,  the  variation  of  stocking  should  show  correlation 
with  the  number  of  trees.    This  was  accordingly  tried. 

From  the  relation  between  mean  diameter  and  total  number  of 
trees  to  the  acre  (figure  6)  it  is  evident  that,  within  the  limits  of  the 
data,  the  mean  diameter  varies  inversely  with  the  number  of  trees. 
This  may  be  checked  by  comparison  of  the  correlation  coefficient, 
r  —  a  measure  of  linear  relationship,  and  the  correlation  ratio  -q  —  a 
measure  of  true  relationship  whether  linear  or  curvilinear,  in  which 

r  =  —  0.80  ±  0.020 
and  >7  =  0.80±  0.020 

showing  that  the  relationship  is  linear. 


BUL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR 


27 


20 


I  . 

c 

«4-  C 

%  ~ 

IS-  in 


1 

o 

\ 

\e 

^ 

^* 

17^ 

N^ 

13 

te 

IS 

^ 

,9 

II 

^4. 

v*^_ 

-^ 

* 

*^o\ 

70        60        30       40       30         20         10    -    0    +    10        20        30        40        50        60        70       SO        90 

Deviation  of  total  number  of  trees  on  plots  from  yield  table.m  per  cent 
Fig.  6. — Kelation  between  mean  diameter  and  number  of  trees  to  the  acre. 


The  relation  between  basal  area  to  the  acre  and  total  number  of 
trees  to  the  acre  is  of  a  different  type.  In  figure  7  it  is  apparent 
that  as  the  number  of  trees  is  increased,  the  basal  area  increases  up 
to  a  certain  point  beyond  which  it  tends  to  fall  off.  That  the  relation- 
ship is  curvilinear  is  brought  out  by  the  difference  between  the 
correlation  coefficient  and  correlation  ratio,  in  which 

r  =  0.439  ±0.044 
v  =  0.540  ±  0.039 

The  peak  of  a  curve  fitted  to  these  data  should  represent  probable 
maximum  stocking  by  basal  area  that  the  species  can  attain,  but  as 
the  course  of  the  plotted  data  is  not  rigidly  defined,  a  free-hand  curve 
is  likely  to  be  too  subjective;  hence  parabolic  regression  is  fitted  by 
the  method  of  moments.13 

The  relation  of  cubic  volume  to  total  number  of  trees  (figure  8) 
is  similar  to  that  of  basal  area  but  is  not  as  strong,  as  indicated  by 
the  following  correlations : 

r  =  —  0.006  ±0.056 
^  =  0.373  ±0.047 


13  Pearson,  Karl.  On  the  general  theory  of  skew  correlation  and  non-linear 
regression.  Mathematical  contributions  to  the  theory  of  evolution  XIV.  Drapers' 
Company  Research  Memoirs,  London  University,    pp.  3-54.    figs.  1-5.    1905. 


28 


UNIVERSITY    OF    CALIFORNIA EXPERIMENT    STATION 


-a     5 


1  - 

3* 

£   S 

O 
*    .0 

o 

(0 

?   80 


*0-23 


30 


ii 

A 

/t 

t 

/I 

v 

i 

\ 

"A 

y 

■-T 

-^ 

\ 

\ 

I6> 

>I3 

4 

> 

7 

i\ 

y 

lol 

13 

r     14 

' 

\ 

^ 

// 

/ 

/ 

/ 

ii 

>  35 

70       60        50        40       30         20        10    -    0    +    10         20       30        HO       SO        60        70        60       QO 

Deviation  of  total  number  of  trees  on  plots  from  yield  table  tr\  per  cent 

Fig.  7. — Eelation  between  basal  area  and  number  of  trees  to  the  acre. 

Greater  variation  in  cubic  volume  for  a  given  number  of  trees  is  due, 
in  part  at  least,  to  greater  variation  in  height  of  trees  in  crown  classes 
below  the  dominant  class. 


o 

c 
"i 
1 


A 

\ 

4 

A 

16 

•& 

\ 

l?N 

Nn, 

6 

v^/ 

A 

\ 

'°\ 

9 

'     3^ 

\ 

\ 

\ 

'    .7 

I   x 

y 

/ ,3 

\ 
\ 

I 

V 

\ 

\ 

\ 

°l 

70       60       30       40       30        20        10   -    0    +    10        20       30        40        50        60       70       60       90 
Deviation  of  total  number  of  trees  on.  plots  from  yield  table, in.  per  cent 

Fig.  8. — Eelation  between  cubic  volume  and  number  of  trees  to  the  acre. 


BUL.  456]  YIELD,  STAND  AND  VOLUME  TABLES  FOR  RED  FIR 


29 


The  effect  of  number  of  trees  on  volume  board  measure  shows  the 
same  general  tendency  (figure  9).   But  since 

r  =  — 0.006  ±  0.056 
and  v  =  0.278  ±0.052 

the  relationship  is  weak,  being  partly  upset,  like  that  of  cubic  volume, 
by  greater  variation  in  height  of  trees  below  the  dominant-crown 
class,  and  partly  by  the  number  of  trees  below  the  8-inch  diameter 
limit  which  do  not  at  all  contribute  to  board-foot  contents. 


1? 

0— 

II 

/ 

/ 
/ 

\ 

i 

16 

\ 

Y 

14- 

4 

0 

A 

V 

,u- 

-*s 

\-r 

^S- 

V 

/ 

t 

13 

ii 

^9\ 

^ 

A 

/  \ 

/ 

\ 

13 

1? 

V 

? 

\ 

\ 

\ 

\ 
\ 

/' 

!  \ 

b 
1 

w 
V 

3 

Fig. 


70       60        50        40       30       20        10   -    O    +    10        £0       30       4-0       50        60       70       SO       90 
Deviation  of  total  number  of  trees  or\  plots  from  yield  table  in  per  cevt 

9. — Relation  between  volume  board  measure  and  number  of  trees  to  the  acre. 


If  the  regressions  as  graphically  shown,  indicate  the  effect  of 
increasing  the  number  of  trees  on  basal  area  and  volume,  then  the 
average  stocking  of  the  basic  plots  as  measured  from  the  maximum 
for  the  species  may  be  judged  by  the  difference  between  the  height 
at  culmination  of  the  curves  and  the  zero  base.  On  these  premises 
yield-table  figures  give  roughly  9  per  cent  less  than  maximum  basal 
area,  6  per  cent  less  than  maximum  cubic  volume,  and  3  per  cent  less 
than  maximum  board  foot  volume.  The  tables,  then,  state  gross- 
volume  close  to  the  productive  possibility  for  red  fir,  and  the  figures 
given  are  attainable  only  when  the  entire  area  is  producing  timber. 


STATION  PUBLICATIONS  AVAILABLE  FOR  FREE  DISTRIBUTION 


BULLETINS 


No.  No. 

253.  Irrigation  and  Soil  Conditions  in  the  389. 

Sierra   Nevada   Foothills,    California.  390. 

262.  Citrus  Diseases  of  Florida  and   Cuba 

Compared  with   those  of   California.  391. 

263.  Size  Grades  for  Ripe  Olives. 

268.   Growing  and  Grafting  Olive  Seedlings.  392. 

277.  Sudan  Grass.  393. 

278.  Grain  Sorghums.  394. 

279.  Irrigation   of   Rice  in   California. 
283.  The  Olive  Insects  of  California. 

304.  A  Study  of  the  Effects  of  Freezes  on  395. 

Citrus  in  California. 

310.  Plum  Pollination.  396. 

313.  Pruning      Young      Deciduous      Fruit 

Trees.  397. 

324.   Storage  of  Perishable  Fruits  at  Freez- 
ing Temperatures.  398. 

328.   Prune   Growing  in   California.  400. 

331.   Phylloxera-resistant  Stocks.  402. 

335.  Cocoanut   Meal    as   a    Feed   for   Dairy  404. 

Cows  and   Other   Livestock.  405. 

340.   Control  •  of     the     Pocket     Gopher     in  406. 

California.  407. 

343.  Cheese   Pests  and  Their   Control. 

344.  Cold   Storage  as   an   Aid   to   the   Mar- 

keting of  Plums,  a  Progress  Report.  408. 

347.  The  Control  of  Red  Spiders  in  Decid-  409. 

uous  Orchards. 

348.  Pruning  Young  Olive  Trees. 

349.  A    Study    of    Sidedraft    and    Tractor 

Hitches.  410. 

350.  Agriculture     in     Gut-Over     Redwood 

Lands. 

353.  Bovine    Infectious    Abortion,    and    As-  411. 

sociated  Diseases  of  Cattle  and  New- 
born Calves.  412. 

354.  Results  of  Rice  Experiments  in  1922. 

357.  A    Self-Mixing    Dusting    Machine    for 

Applying  Dry  Insecticides  and  Fun-  414. 

gicides. 

358.  Black    Measles,     Water    Berries,     and  415. 

Related  Vine  Troubles.  416. 

361.  Preliminary  Yield  Tables  for  Second- 

Growth   Redwood.  417. 

362.  Dust  and  the  Tractor  Engine. 

363.  The  Pruning  of  Citrus  Trees  in  Cali-  418. 

fornia. 

364.  Fungicidal   Dusts   for   the    Control    of  419. 

Bunt. 

366.  Turkish     Tobacco     Culture,     Curing,  420. 

and  Marketing. 

367.  Methods  of  Harvesting  and  Irrigation  421. 

in  Relation  to  Moldy  Walnuts.  422. 

368.  Bacterial      Decomposition      of      Olives 

During  Pickling.  423. 

369.  Comparison     of     Woods     for     Butter 

Boxes.  424. 

370.  Factors    Influencing   the    Development 

of  Internal  Browning  of  the  Yellow  425. 

Newton  Apple.  426. 

371.  The    Relative   Cost   of   Yarding    Small 

and  Large  Timber.  427. 

373.  Pear   Pollination. 

374.  A    Survey    of    Orchard    Practices    in  428. 

the     Citrus     Industry     of     Southern 
California. 

375.  Results   of    Rice   Experiments   at   Cor-  429. 

tena,  1923,  and  Progress  in  Experi-  430. 

ments  in  Water  Grass  Control  at  the  431. 

Biggs  Rice  Field   Station,    1922-23. 
377.  The  Cold  Storage  of  Pears.  432. 

380.   Growth    of    Eucalyptus    in    California 

Plantations.  433. 

382.   Pumping    for    Draininge    in    the    San 

Joaquin   Valley,    California.  434. 

385.  Pollination  of  the  Sweet  Cherry. 

386.  Pruning     Bearing     Deciduous     Fruit  435. 

Trees. 

387.  Fig   Smut. 

388.  The   Principles   and   Practice   of    Sun- 

Drying  Fruit. 


Berseem  or  Egyptian  Clover. 

Harvesting  and  Packing  Grapes  in 
California. 

Machines  for  Coating  Seed  Wheat 
with   Copper  Carbonate   Dust. 

Fruit  Juice  Concentrates. 

Crop   Sequences  at  Davis. 

I.  Cereal  Hay  Production  in  Cali- 
fornia. II.  Feeding  Trials  with 
Cereal  Hays. 

Bark  Diseases  of  Citrus  Trees  in  Cali- 
fornia. 

The  Mat  Bean,  Phaseolus  Aconitifo- 
lius. 

Manufacture  of  Roquefort  Type  Cheese 
from  Goat's  Milk. 

Orchard   Heating  in   California. 

The  Utilization  of  Surplus  Plums. 

The  Codling  Moth  in  Walnuts. 

The  Dehydration  of  Prunes. 

Citrus   Culture   in    Central   California. 

Stationary  Spray  Plants  in  California. 

Yield,  Stand,  and  Volume  Tables  for 
White  Fir  in  the  California  Pine 
Region. 

Alternaria  Rot  of  Lemons. 

The  Digestibility  of  Certain  Fruit  By- 
products as  Determined  for  Rumi- 
nants. Part  I.  Dried  Orange  Pulp 
and  Raisin  Pulp. 

Factors  Influencing  the  Quality  of 
Fresh  Asparagus  after  it  is  Har- 
vested. 

Paradichlorobenzene  as  a  Soil  Fumi- 
gant. 

A  Study  of  the  Relative  Value  of  Cer- 
tain Root  Crops  and  Salmon  Oil  as 
Sources   of   Vitamin   A  for   Poultry. 

Planting  and  Thinning  Distances  for 
Deciduous  Fruit  Trees. 

The  Tractor  on   California  Farms. 

Culture  of  the  Oriental  Persimmon  in 
California. 

Poultry  Feeding:  Principles  and  Prac- 
tice. 

A  Study  of  Various  Rations  for  Fin- 
ishing Range  Calves    as  Baby  Beeves. 

Economic  Aspects  of  the  Cantaloupe 
Industry. 

Rice  and  Rice  By-Products  as  Feeds 
for  Fattening  Swine. 

Beef   Cattle  Feeding  Trials,    1921-24. 

Cost  of  Producing  Almonds  in  Cali- 
fornia: a  Progress  Report. 

Apricots  (Series  on  California  Crops 
and  Prices). 

The  Relation  of  Rate  of  Maturity  to 
Egg  Production. 

Apple  Growing  in  California. 

Apple  Pollination  Studies  in 
fornia. 

The  Value  of  Orange  Pulp  for 
Production. 

The  Relation  of  Maturity  of 
fornia  Plums  to  Shipping 
Dessert  Quality. 

Economic  Status  of  the  Grape  Industry. 

Range  Grasses  of  California. 

Raisin  By-Products  and  Bean  Screen- 
ings as  Feeds  for  Fattening  Lambs. 

Some  Economic  Problems  Involved  in 
the  Pooling  of  Fruit. 

Power  Requirements  of  Electrically 
Driven    Manufacturing    Equipment. 

Investigations  on  the  Use  of  Fruits  in 
Ice  Cream  and  Ices. 

The  Problem  of  Securing  Closer 
Relationship  Between  Agricultural 
Development  and  Irrigation  Con- 
struction. 


Cali- 
Milk 


Cali- 
and 


No. 

436.  I.   The   Kadota   Fig.      II.   Kadota   Fig 

Products. 

437.  Economic    Aspects    of    the    Dairy    In- 

dustry. 

438.  Grafting  Affinities  with  Special  Refer- 

ence to  Plums. 

439.  The  Digestibility  of  Certain  Fruit  By- 

products as  Determined  for  Rumi- 
nants. Part  II.  Dried  Pineapple 
Pulp,  Dried  Lemon  Pulp,  and  Dried 
Olive  Pulp. 

440.  The    Feeding    Value    of    Raisins    and 

Dairy  By-Products  for  Growing  and 
Fattening  Swine. 

441.  The  Electric  Brooder. 

442.  Laboratory  Tests  of  Orchard  Heaters. 

443.  Standardization    and    Improvement    of 

California   Butter. 

444.  Series  on  California  Crops  and  Prices: 


B  ULLETI NS—  ( Continued) 
No. 


445.  Economic    Aspects    of    the    Apple    In- 

dustry. 

446.  The  Asparagus  Industry  in  California. 

447.  The  Method  of  Determining  the  Clean 

Weights    of    Individual    Fleeces    of 
Wool. 

448.  Farmers'      Purchase     Agreement     for 

Deep   Well   Pumps. 

449.  Economic   Aspects  of  the  Watermelon 

Industry. 

450.  Irrigation    Investigations    with    Field 

Crops  at  Davis,   and  at  Delhi,   Cali- 
fornia. 

451.  Studies    Preliminary   to   the   Establish- 

ment of  a  Series  of  Fertilizer  Trials 
in  a  Bearing  Citrus  Grove. 

452.  Economic    Aspects    of    the    Pear    In- 

dustry. 


CIRCULARS 

No.  No> 

87.   Alfalfa.  265, 

117.  The    selection    and    Cost    of    a    Small  266. 

Pumping   Plant. 

127.   House  Fumigation.  267 
129.  The  control  of  Citrus  Insects. 

136.   Melilotus    Indica    as    a    Green-Manure  269. 

Crop  for  California.  270. 

144.   Oidium    or    Powdery    Mildew    of    the  273. 

Vine.  276 

157.   Control   of   Pear   Scab.  277 
164.   Small   Fruit    Culture    in    California. 

166.  The  County  Farm  Bureau.  278 
178.  The  Packing  of  Apples  in   California. 

202.  County    Organization    for    Rural    Fire  279. 

Control. 

203.  Peat   as   a  Manure   Substitute.  281 
209.  The  Function  of  the  Farm  Bureau. 

212.   Salvaging  Rain-Damaged  Prunes. 

215.  Feeding  Dairy  Cows  in   California.  282 

230.  Testing  Milk,    Cream,    and   Skim  Milk 

for  Butterfat.  284. 

231.  The   Home   Vineyard.  286. 

232.  Harvesting    and    Handling    California  287! 

Cherries   for   Eastern    Shipment.  288. 

234.  Winter     Injury     to     Young     Walnut  289 

Trees  During  1921-1922.  290. 

238.  The   Apricot  in   California.  292! 

239.  Harvesting     and     Handling     Apricots  293. 

and  Plums  for  Eastern  Shipment.  294! 

240.  Harvesting    and    Handling    California  296! 

Pears  for  Eastern  Shipment. 

241.  Harvesting    and    Handling    California  298. 

Peaches  for  Eastern   Shipment. 

243.  Marmalade     Juice     and     Jelly     Juice  300. 

from  Citrus  Fruits.  301. 

244.  Central  Wire  Bracing  for  Fruit  Trees.  302. 

245.  Vine  Pruning   Systems.  304! 

248.  Some  Common  Errors  in  Vine   Prun-  305! 

ing  and  Their  Remedies.  307. 

249.  Replacing  Missing  Vines.  308. 

250.  Measurement  of   Irrigation   Water   on  309! 

the  Farm.  310. 

252.  Support  for   Vines. 

253.  Vineyard  Plans.  311. 
255.   Leguminous    Plants    as    Organic    Fer-  312. 

tilizers  in   California   Agriculture. 

257.  The   Small-Seeded   Horse  Bean    (Vicia 

faba   var.   minor). 

258.  Thinning   Deciduous   Fruits. 

259.  Pear  By-Products. 
261.   Sewing  Grain  Sacks. 


Plant   Disease  and  Pest  Control. 

Analyzing  the  Citrus  Orchard  by 
Means  of  Simple  Tree  Records. 

The  Tendency  of  Tractors  to  Rise  in 
Front;  Causes  and  Remedies. 

An   Orchard   Brush  Burner. 

A  Farm  Septic  Tank. 

Saving  the  Gophered  Citrus  Tree. 

Home   Canning. 

Head,  Cane  and  Cordon  Pruning  of 
Vines. 

Olive  Pickling  in  Mediterranean 
Countries. 

The  Preparation  and  Refining  of 
Olive  Oil  in  Southern  Europe. 

The  Results  of  a  Survey  to  Deter- 
mine the  Cost  of  Producing  Beef  in 
California. 

Prevention  of  Insect  Attack  on  Stored 
Grain. 

The  Almond  in   California. 

Milk  Houses  for  California  Dairies. 

Potato   Production  in   California. 

Phylloxera  Resistant  Vineyards. 

Oak  Fungus  in   Orchard  Trees. 

The  Tangier  Pea. 

Alkali   Soils. 

The    Basis   of   Grape    Standardization. 

Propagation   of   Deciduous  Fruits. 

Control  of  the  California  Ground 
Squirrel. 

Possibilities  and  Limitations  of  Coop- 
erative Marketing. 

Coccidiosis  of  Chickens. 

Buckeye  Poisoning  of  the  Honey  Bee. 

The   Sugar  Beet  in  California. 

Drainage  on  the  Farm. 

Liming  the   Soil. 

American   Foulbrood   and   Its  Control. 

Cantaloupe    Production   in   California. 

Fruit  Tree  and  Orchard  Judging. 

The  Operation  of  the  Bacteriological 
Laboratory  for  Dairy  Plants. 

The  Improvement  of  Quality  in  Figs. 

Principles  Governing  the  Choice,  Op- 
eration and  Care  of  Small  Irrigation 
Pumping   Plants. 


The  publications  listed  above  may  be  had  by  addressing 

College  of  Agriculture, 

University  of  California, 

Berkeley,  California. 


8m-9  ,'28 


